Shall We Keep Early Diers Alive?

Andrea PinnaQueen Mary, University of London

and Free University of Bozen-Bolzano

This Version: November 2014

Abstract

Most extant explanations of financial crises emphasise the roleplayed by negative shocks on the liability side of a bank’s balancesheet. The vast literature on bank runs induced policy makersto build up a reputation as institutions willing to do anythingto support the orderly fulfillment of depositors’ and interbankclaims. Nonetheless, the LTCM crisis of 1998 and the Subprimecrisis of 2007 are compelling examples of how the banking in-dustry is prone to systemic disruptions even without preferenceshocks or domino effect. This survey argues in favour of the stillmarginal literature on financial crises unfolding through the as-set side of banks’ balance sheets.

JEL Classification: G01, G32.Keywords: Financial crises, Originate to distribute, Shadow bank-ing, Diabolic loop.

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1 Introduction

Taking the cue from the 2007-2009 Subprime crisis, this chapter pro-poses an overview of the literature on bank runs and financial conta-gion. Some pathbreaking models are examined to emphasise a slow butdecisive shift of the literature, which started by addressing the issueof preferences shocks and is now focusing on the impact the access tocollateralized borrowing has on the banking industry.

The following stylised facts are among those justifying the new ap-proach:- Banks increasingly invested outside their traditional loans activity,holding huge amounts of structured products that are continuouslytraded on financial markets and used to raise liquidity- Banks transfer opaque structured products to other financial institu-tions in order to reduce the cost risky investments have in terms ofreserves.- A surge in the delinquency rate of a relatively small portion of loansin 2007 decreased worldwide liquidity.- Public institutions struggled to sustain banks funding capacity throughinjections of liquidity.

Banks provide a valuable insurance to depositors who are uncertainabout the time of their consumption needs. They do so by offeringdeposit contracts and using some of the proceeds to invest in illiquidassets. The necessity that the banking industry may perform such avaluable task without jeopardising the real economy justified an ex-tensive research on the topic of financial stability. The modern litera-ture on financial crises dates back to the early eighties and spread in anumber of works the present paper does not attempt to consider thor-oughly. The seminal work by Bryant (1980) and its formalisation byDiamond and Dybvig (1983), focused on models with one representa-tive bank. These works emphasized the fragility of financial institu-tions facing a temporary gap between realizations of assets (long-termloans) and liabilities (short-term deposits). Early papers insisted on theweaknesses bank deposit contracts bring about. Allen and Gale (1988),Goldstein and Pauzner (2005), and Jacklin and Bhattacharya (1988)enriched the analysis linking depositors’ expectations to the business-cycle. Adrian and Shin (2010), Allen and Gale (2000, 2004), Brusco

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and Castiglionesi (2007), Cifuentes et al. (2005), Diamond and Rajan(2005), Freixas et al. (2000), Rochet and Vives (2004), although keep-ing much of their framework in the very same vein as previous modelson bank runs, singled out what channels the run on one bank maytrigger a financial crisis through. The latest developments in the mod-elling of financial crises are related to the ongoing Eurozone sovereignand banking crisis. Work by Acharya et al. (2011), Bolton and Jeanne(2011), Brunnermeier et al. (2011), Gennaioli et al. (2014), Gerlach et al.(2010), Mody and Sandri (2012), Panetta et al. (2011) and Popov andVan Horen (2013) addresses the interconnection among sovereigns andthe banking sector, showing that it may channel both domestic andcross-border contagion.

I follow in Section 2 the traditional taxonomy of the literature onbank runs, emphasising differences among the “coordination failure”and the “business-cycle” interpretations of the phenomenon. In Sec-tion 3, models of contagion relying on the early withdrawal by somedepositors are reviewed, and their adequacy in accounting for modernfinancial crises is disputed. Section 4 focuses on a more recent approachto contagion, whereby a crisis spreads through the asset side of bankbalance sheet. Section 5 addresses the ongoing Eurozone sovereign andbanking crisis. Section 6 concludes.

2 Bank Runs

The theoretical research on bank runs and financial crises is of particu-lar importance because of its relevance for decisions of both regulatorsand investors. This induced a vast and diverse literature that evolvedtogether with business models and financial innovation over the last 30years. Its usual taxonomy is based on what kind of uncertainty triggersthe insolvency of a financial institution. On the one hand, the sunspotapproach assumes runs are caused by a shift in depositors’ beliefs thatis unrelated to the real economy. On the other hand, the business-cycleapproach assumes that such a shift is due to shocks affecting economicvariables.

In all models of bank runs, financial difficulties stem from the samefriction: due to the illiquid nature of entrepreneurial projects, a bankis exposed to depositors’ early claims over assets that cannot be easily

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converted into cash. These depositors act as “early diers”and want towithdraw their deposits immediately. Whenever such maturity mis-match stretches withdrawals to a level the bank did not expect, thecostly liquidation of long-term assets makes the value of a bank portfo-lio inadequate to meet liabilities. This induces even patient consumersto withdraw their money, as long as their bank has any value to pay outand before other fellow depositors seize it. Therefore, the mismatch be-tween withdrawals and bank liquidity worsens.

2.1 Panic Runs

The sunspot view of bank runs suggests that withdrawals exceed theirex ante expected level because of self-fulfilling prophecies on exogenousevents. In the three-period model of Diamond and Dybvig (1983), con-sumers are uncertain about the timing of their consumption needs.Banks are modelled as risk-sharing institutions that pool consumers’endowments at the initial date and invest them in a portfolio of long-and short-term assets. Since the focus of the model is on a bank liabili-ties rather than assets, the latter are simply risk-free investments payinga strictly positive return R if held over two periods. If the investmentis liquidated after one period it pays no return, likewise the short-termstorage technology. The bank offers depositors a contract allowing toreceive either a fixed claim r1 at date 1 or r2 at date 2, in exchange fortheir endowment. Consumers are all identical ex ante, but each of themfaces the privately observable risk of being an “early dier”who valuesimmediate consumption only. Every consumer has the following state-dependent utility function:

U (c1, c2;θ) = {u(c1) if the consumer is an early dier in state θ;ρu(c1+c2) otherwise.

Where ci denotes the level of consumption at date i , 1 ≥ ρ > R−1 andu(·) is increasing, concave and satisfies the Inada conditions. In sucha framework, the consumption path depositors choose may be mis-matched with the timing of banks return on investments. There is freeentry into the banking sector, thus banks maximise the expected utilityof depositors in order to attract more customers. The way they do so isby providing agents with insurance against their idiosyncratic liquidity

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risk. If the bank knows the number of early consumers, optimal risk-sharing is attainable. Under asymmetric information, however, anyrisk-sharing contract with r1 > 1 allows early withdrawers to claim liq-uidity on illiquid assets at the interim date. Since the bank is exposed toshort-term claims over long-term assets, there is a multiplicity of equi-libria that allows the prophecy of a bank run to be self-fulfilling. Theamount of consumption c2 a depositor can get at date 2 depends in facton how much a bank has to liquidate of its long-term investments, tosatisfy early withdrawals at date 1. If some late depositors predict thatmore than the expected number of early diers withdraw their liquidityat the interim date, under a first-come first-served rule it is optimal forthem to do the same. But then it is true that more than the ex ante ex-pected number of early depositors take out their money at the interimdate. It is therefore a best response for all late consumers to withdrawimmediately, so that a run happens. Patient consumers would prefer toleave their liquidity with the bank if there were no unexpected with-drawals. However, they know there might be early withdrawals andtheir place in line matters to avoid facing the loss of their endowment.By contrast, no patient consumer attempts to withdraw his funds earlyif everybody believes no panic is about to occur. In such a case, bankassets satisfy both the liquidity needs of investors who are hit by the liq-uidity shock and those of patient depositors who wait for the paymentof long-term investments.

When a bank run happens, some depositors who needed to satisfyan early liquidity need find themselves short of the cash they needed,whereas patient consumers have more cash than they need and cannotenjoy the higher return on long-term investments. Thus, consumers’welfare is not maximised. The focus of this thesis is on the microe-conomic foundation of banking crises. However, it is natural that re-search on financial instability aims to derive run-preventing contractsand to perform welfare analysis. The results by Diamond and Dybvig(1983) are unsatisfactory in that respect. In fact, investment and depositcontract are chosen ex ante by banks that hope the good equilibriumwill be achieved. Were the bank, or the regulator, able to anticipate apanic, they might take different decisions to avoid the run. Yet, theissue of what event causes depositors to run on their bank is not ad-dressed, and banks simply turn out to be inherently unstable institu-

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tions. Furthermore, when one widens the focus from a single bank tothe financial system, it is necessary to find sunspots hitting all banks atonce to justify a system-wide financial crisis.

Despite these shortcomings, the Diamond and Dybvig (1983) ap-proach has been the most influential one to address the issue of financialinstability. The vast majority of later work on the topic still borrowstwo main elements from such approach: (1) early diers determine unex-pected demand for liquid assets, (2) patient consumers may misreporttheir type, to win the run on the bank and get their claims satisfied.

2.2 Fundamental Runs

Gorton (1988) conducts an empirical study to assess whether bank runsare systematically linked to the business-cycle, rather than being reac-tions to extrinsic uncertainty. Using the liabilities of failed nonfinan-cial businesses as the leading economic indicator, he finds that panicsare systematic events that come at or near business cycle peaks.

In business-cycle models of bank runs, depositors react to new in-formation. News are not specific to their own bank, but are deemedrelevant in the assessment of its reliability. Thus, a run starts only ifnew information disputes the ability for a bank assets to meet its li-abilities. When a shock endangers the solvency of a bank, depositorsperceive the latter as riskier and may decide to withdraw their funds be-fore other depositors claim the whole (insufficient) liquidity their bankis able to pay out early.

Jacklin and Bhattacharya (1988) modify the Diamond and Dybvig(1983) model and relate panics to the business-cycle. They emphasisethe role depositors’ information at an interim date can play in causinga bank run. The return on long-term investments is a random variabledepositors receive interim information about. New information mayinduce patient consumers to mimic early diers who run the bank toclaim their liquidity.

Allen and Gale (1988) model interim information similarly to Jack-lin and Bhattacharya (1988). Their analysis is richer as they considerthe opportunity for late consumers to access the same technology thatis available to banks. On the one hand, the authors find out thatbank runs can achieve optimal risk sharing between early and late con-

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sumers. Such result arises if early liquidation does not affect the returnon assets, and the liquidity is split among withdrawers on an equal basisrather than sequentially. On the other hand, if the asset is liquidatedearly at a loss and consumers cannot attain the same return on invest-ment as their banks do, the fraction of late consumers who mimic earlydiers affects the total amount of available consumption and a run oc-curs.

2.3 Global Games

Models of bank run relying on coordination failures account for bigeffects following small shocks. Such a feature is typical of financialcrises. Nevertheless, this work relies on extrinsic uncertainty and is oflittle help for policy makers. The business-cycle explanation accountsfor the rationale underlying a run, but it rules out the possibility thata crisis is triggered by a small unexpected shock. The fact that a jumpin the economy-wide performance is necessary to unleash a run makesthe latter unlikely to happen.

The global games approach, developed by Carlsson and Van Damme(1993), combines the panic and the business-cycle views of bank runs.Such a technique links the probability of occurrence of a crisis to signalsdepositors get, at an interim date, about the future state of the world.

Frankel et al. (2003) show that the uniqueness of equilibrium forgames with many players relies on the assumption of global strate-gic complementarities. Namely, agents’ incentive to undertake an ac-tion increases monotonically with the number of other agents engag-ing in the same action. Under such assumption the technique providestestable predictions on whether real shocks are able to trigger a run,although the latter still stems from coordination failures.

Rochet and Vives (2004) introduce global strategic complementar-ities in a model where banks face the threat of a run by early diersà la Diamond and Dybvig. The authors assume investors cannot de-posit their endowments in a bank without the intervention of inter-mediaries. The latter make the decision of withdrawing monotonic inthe number of agents who take the same action, via a reputation ef-fect linked to the acknowledgement of any wrong investment. An assetmanager withdraws his investment only if the probability of failure of

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the bank, conditioned to the signal and the behaviour he expects fromthe other managers, is sufficently high. This leads to the followingequilibrium: if the signal about assets return is poor, bank failures arecaused by insolvency; if the signal is good, failures caused by illiquiditymay still occur only if many other managers are expected to withdraw.

Goldstein and Pauzner (2005) enrich the Diamond and Dybvig (1983)model, allowing the fundamentals of the economy to determine wheth-er a bank run occurs. To obtain a unique equilibrium, they show thatthe uniqueness result adopted by Rochet and Vives (2004) can be gener-alised to a framework where strategic complementarities are one-sided.This means that the incentive to withdraw increases with the numberof agents who do so, only as long as the latter are few enough to makethe waiting strategy preferred to that of withdrawing. The authors fo-cus on depositors’ decisions rather than banks, allowing individuals toobtain noisy private signals on the fundamentals of the economy. Theequilibrium result is unique and leads to a bank run only when the rel-evant economic indicators are lower than a threshold value. Runs arestill triggered by bad expectations giving incentive to mimic early diers,like in panic models, but the fundamentals of the economy determinewhether expectations are compatible with a bank run. This allows theauthors to find a probability for panic-based run, and to relate such ameasure to the performance of the economy as well as to the terms ofthe deposit agreement.

3 Domino Financial Crises

Hitherto revised models – based on either self-fulfilling prophecy, rev-elation of new information, or signalling problems – are focused on asingle institution. These suggest what may start a crisis, but cannotaccount for contagion.

Bhattacharya and Gale (1987) introduce an interbank market in theDiamond and Dybvig (1983) model, to study the impact preferenceshocks have on the whole industry when banks are allowed to tradeliquidity. In their model, a bank does not know the proportion of earlydiers among its depositors. With no aggregate uncertainty, the oppor-tunity for trading liquidity at the interim date allows each institutionto hedge against region-specific shocks. Such a market for liquidity

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lowers the probability of a bank run, since illiquid banks can borrowfrom cash-awashed regions. Nevertheless, it introduces the possibilitythat a local shock affects the whole industry. The issue is typical ofmoral hazard: banks have an incentive to underinvest in costly liquid-ity and attempt to get it, only when it is necessary, from other peersof the interbank market. The presence of overlapping claims amongbanks can then produce a domino effect when the industry is hit by sys-temic shortages, with the bankruptcy of any institution dragging downall other peers of the network. A regulator cannot perfectly monitorbanks’ investment decision and, if a crisis occurs, the liquidity it mayinject does not necessarily flow to institutions who need it.

After Bhattacharya and Gale (1987), many authors emphasised therole interbank markets play in propagating a crisis through overlap-ping claims. Allen and Gale (2000) study the impact the topology of aninterbank market has on the risk of contagion. They consider a versionof the Diamond-Dybvig model in a multi-region economy, wherein theproportion of early diers is random and negatively correlated across re-gions. In such a framework, the interbank market plays for banks thesame role any bank plays for depositors in models of bank runs: itpools its users’ resources to insure them against idiosyncratic shocks.In both cases, when there is no aggregate uncertainty, the first-best al-location of risk sharing can be achieved. However, if aggregate liquid-ity is scarce, interbank linkages provide a channel the shock affectinga bank can propagate through. Institutions that are hit by unexpectedwithdrawals at the interim date can avoid liquidating long-term invest-ments, since imperfect correlation allow them to demand cash frombanks in regions with liquidity in excess. When the phenomenon is re-versed at the following date, claims of banks hit in different dates cancelout on average. If the shock is a systemic one, the only way a bank hasto provide more consumption after claiming all interbank deposits isto liquidate the long-term asset. Thus, late consumers are induced torun on their bank. Allen and Gale (2000) show that the probability ofcontagion depends on the architecture of the interbank market: if ev-ery region is connected with the others, the initial impact of long-termassets liquidation may be attenuated and contagion avoided. On thecontrary, if each region is connected with few others, the impact of theinitial liquidation is strong in the closer regions.

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Brusco and Castiglionesi (2007) investigate the same issue as Allenand Gale (2000) in a different multi-region economy. They account formoral hazard among regional banks and find a result that is diametri-cally opposite to that of Allen and Gale. Furthermore, in their modela financial crisis can precipitate even with no aggregate uncertainty.Consumers are the standard Diamond and Dybvig (1983) ones, withadditional uncertainty on what region faces the higher proportion ofearly diers. The key assumptions that introduce moral hazard in themodel are two: (1) differently from all models reviewed so far, financialinstitutions aim to maximise dividend payments rather than deposi-tors’ utility; (2) the investment technology allows banks to appropriatean unobservable part of the return and hide information on their long-term investments. Banks can choose among two different long-terminvestments: a safer asset and a riskier one, the latter yielding a neg-ative expected rate of return. Investing in the riskier assets becomesattractive if banks, protected by limited liability, are undercapitalisedand gamble with depositors’ money. It turns out that depositors mayfind it optimal to choose a contract allowing their bank to engage in as-set substitution, to enjoy a higher return from long-term assets. In fact,since the possibility that the riskier asset defaults is known at the finaldate, the liquidity coinsurance provided from an interbank market al-lows early diers to have their claims met, as long as the bank is ableto borrow from other banks the liquidity it needs. At the final date,two outcomes may arise: if the bank who gambled is the one who lentmoney at the previous date, it goes bankrupt without affecting otherbanks; if the gambling bank was a borrower, its wrong bet trails lendersto default. Thus, although a network benefits depositors through liq-uidity coinsurance, such a benefit is potentially offset by their leniencyand the cost of a greater exposure to systemic crises.

Freixas et al. (2000) model an interbank market that allows depos-itors to hedge against uncertainty on where they need to consume.Each regional bank is therefore uncertain about the amount of with-drawals it will deal with, and the interbank payment system insuresagainst such a risk. However, if depositors in one region believe theirdestination will be liquidity-constrained, their best response is to be-have as early diers at home and to carry the liquidity they need. Thisforces the local bank to liquidate its long assets early at a loss and, by

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backward induction, the liquidation makes it optimal for depositors inother locations to withdraw all money they need for consumption inthe first region. The interbank market may thus expose the industryto inefficient financial crises just because some depositors, who do nottrust other financial institutions, trigger a run on their own bank.

Empirical research shows that interbank linkages are too weak tospread contagion as the theoretical literature suggests. Sheldon andMaurer (1998), Upper and Worms (2004), and Furfine (2003) estimatethe matrix of bilateral exposure among banks in Switzerland, Germanyand the US, respectively. They simulate the extent of contagion causedby the default of a single bank. Given their results, a domino effectdoes not explain the occurrence of the Subprime crisis.

4 Asset-Side Contagion

Models of domino contagion rely on banks’ inability to meet their li-abilities with depositors. Such approach reflects the importance bankshave as insurance providers to their depositors, and the role played byan interbank market. Nevertheless, it accounts for passive financial in-stitutions, who stand by and do nothing as the sequence of defaultsunfold. Throughout the previous sections, asset prices were assumedto be unaffected by the crisis. Such a view does not consider the effectof market forces and mark-to-market accounting. The impact of pricechanges on the book value of banks’ assets magnifies the adverse impactof counterparties’ defaults.

Allen and Gale (2004), Diamond and Rajan (2005), and Cifuenteset al. (2005) show that the interaction among changes in asset pricesand solvency requirements amplifies any initial shock. An immedi-ate consequence of a bank default is that the liquidation of its long-term investments causes the deflation of their price, if the market isnot perfectly liquid. Other banks may react to the reduction in thevalue of their marked-to-market balance sheet by selling their assets, toavoid breaching their commitments with depositors (deposit contract),money market funds (margin calls), and regulators (risk constraints).Sales induce a further decline in assets value, which may outweigh theeffect of the initial reaction.

To account for such a phenomenon, one needs to single out a proper

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source of friction in the financial market. Shleifer and Vishny (1992)describe fire sales – namely trades of an asset at prices below its fairvalue – when financial distress clusters through time in a generic indus-try where firms hold specialized assets. When a firm must sell its assetsbecause of financial distress, potential buyers with the highest valuationare other firms in the same industry, who are likely to be in a similarfinancial situation and may therefore be unable to offer enough liquid-ity. The same account fits financial markets: because of asymmetricinformation or specialised investments strategies, outsiders are willingto pay for the asset less than its industry-specific value. According toAcharya et al. (2012) a bank with market power may even provide in-sufficient lending strategically, to make liquidity-constrained banks selltheir industry-specific asset so that it can take advantage of lower assetprices.

Adrian and Shin (2010) show that marked-to-market leverage is stron-gly procyclical. The authors document that institutional investors, dif-ferently from households, respond to changes in the value of their port-folio by moving leverage in the same direction as the market. Thus,instotutional traders amplify the price trend by selling when pricesslump and amplify the price trend. Allen and Gale (2004) build onAllen and Gale (2000) to show how such a behaviour allows smallpreference shocks to precipitate a crisis through self-reinforcing pricechanges. The key elements in the model are (1) the role liquidity playsin determining asset prices and (2) its interaction with three sources ofintrinsic uncertainty, all resolved at the interim date: consumers havethe usual random preferences à la Diamond and Dybvig (1983); theproportion of early diers in the economy is unknown; and each bankdoes not know the fraction of early diers it must deal with. Similarlyto Allen and Gale (2000), banks facing higher than expected demandfor liquidity at the interim date can smooth both their wealth and de-positors’ consumption over time by selling long-term assets to banksfacing an unexpectedly low demand. The supply of liquidity in theshort run is given by banks’ portfolio decisions at the initial date. Inan incomplete financial market, lenders cannot be remunerated contin-gent to the cost of providing liquidity in all states. Therefore, the priceof long-term assets when liquidity is needed has to be sufficiently highto compensate the opportunity cost of holding liquidity when there

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is no liquidity shock. Substantial sales determine cash-in-the-marketpricing. As prices fall, any bank needs to sell an even larger proportionof its long-term assets. This can lower asset prices to an extent thatprevents the institution from satisfying its commitments even when alllong-term assets are liquidated. With the new lower asset prices, otherbanks need selling as well and put asset prices under further pressure.Thus, even small shocks can trigger a systemic crisis. Although the re-sult is similar to that of Allen and Gale (2000), contagion occurs withno prespecified interbank linkage. The channel for contagion is pro-vided by the spot market via a downward spiral in asset prices.

Diamond and Rajan (2005) analyse the same type of contagion asAllen and Gale (2004) in a general equilibrium model wherein the onlyassets in the economy, entrepreneurial loans, pay off at an uncertaindate. If the number of assets that pay late is low enough, the bankingindustry has the available liquidity it needs to fulfill claims by earlydiers. Although the demand for liquidity at the interim date exceeds itsex-ante expected value, a bank can in fact raise liquidity by selling late-realization assets to entrepreneurs whose projects pay early. The latterhold some excesse liquidity after the repayment of their loans. Thus,banks manage to allocate efficiently what entrepeneurs produce at theinterim date, and the market allows absorbing the initial shock. On theother hand, if too many projects are delayed, any bank whose realisedassets are inadequate to fulfil early withdrawals sells late-realization as-sets on an illiquid market. If the value of such assets is insufficient toraise enough liquidity, the bank may increase the interest rate on de-posits. This attracts depositors from other banks but does not solvethe aggregate shortage. Furthermore, banks’ asset value drops wheninterest rates increase. Before banks produce the desired amount of ag-gregate liquidity by restructuring late projects, the self-reinforcing fallin prices may start a chain of defaults.

Whereas all models analysed thus far relied on preferences shocksto account for a bank run, Cifuentes et al. (2005) refrain from charac-terising what kind of shock hits the economy. The authors focus onhow solvency constraints create liquidity risk in a system of intercon-nected financial institutions, when the latter mark their assets to mar-ket. Their model extends the main intuition of Shleifer and Vishny(1992) to the banking industry, wherein a shock on assets value makes

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a bank violate its solvency constraint. The endangered bank must sellpart of its assets and that, since the demand for the asset is less thanperfectly elastic, lowers prices. Solvency constraints may then dictatefurther disposals and lead the banking sector to collapse, without needfor either preference shocks or late consumers mimicking early diers.

The LTCM crisis of 1998 is a compelling example of how far a crisismay spread from the balance sheet of a financial institution, withoutany preference shock. When the value of LTCM’s capital fell from $7billions to $0.6 billion one month after the Russian government re-structured its debt, the Federal Reserve Bank of New York arrangedfor a group of private banks to purchase the endangered fund and liqui-date its positions without fire sales. LTCM raised big concern becauseit held many large positions in illiquid assets, whose price drop wouldaffect other institutions. Notwithstanding the awareness financial regu-lators have of the possibility for financial crises to occur from the mereasset side of the financial market, most extant explanations of financialcrises emphasise the negative externalities on the liabilities side of thebalance sheet: it is the run by depositors that precipitates the crisis.

4.1 Modelling the Subprime Crisis

By virtue of the policies suggested over three decades of research, cen-tral banks managed to relegate demand-driven bank crises to break outin text books more often than in newspapers. Such a phenomenoncame back in 2007 in the UK, one century after the previous bank runin the British banking system, when customers queued to withdrawtheir deposits in Northern Rock. The Subprime crisis, able to set offsuch secular event, questioned our understanding of financial crises. Itdoes not fit either the account given by models relying on self-fulfillingprophecies or those stemming from domino effects.

Early diers do not seem to have played a primary role in the crisis: tobegin with, banks got in trouble before anything happened to liquid-ity demand, and they kept the bad news secret as long as they could.1

1Shin (2009) reports on the run to Northern Rock: “The Bank of England was in-formed [of Northern Rock’s funding problems] on August 14th. From that time untilthe fateful announcement on September 14th that triggered the deposit run (i.e. for afull month), the Financial Service Authority and Bank of England sought to resolve

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Furthermore, central banks have now succeeded in appearing ready todo anything for the sake of financial stability. Thus, a consumer panic,either driven by phrophecies, interim signals or asymmetric informa-tion, does not give a satisfactory explanation to the extent of the crisis.

In force of central banks attitude, the present work calls for a changeof focus towards contagion mechanisms wherein depositors do not careabout drops in banks’ portfolio value. They are conscious that theircentral bank and public insurance on deposits will keep deposits safe.This approach allows to focus the analysis on the consequences marketfluctuations and risk constraints have on banks solvency.

Diamond and Rajan (2011) show that the overhang of illiquid assetsincreases the future return of holding them in the eve of fire selling.Opaque Asset Backed Securities (ABSs) are likely to depreciate much,since only few specialized firms can evaluate them. Thus, the prospectof buying undervalued assets in the near future induces an endangeredbank to hold them hoping they will appreciate before breaching itscommitments.

Heider et al. (2009) model an interbank market where financial insti-tutions lend money to each other in order to deal with the traditionalissue of early diers. The authors introduce asymmetric informationabout counterparty risk among banks. The private information eachbank has on its risky investment produces adverse selection. This canlead the unsecured interbank market to freeze, because lenders hoardliquidity and the cost of the latter becomes too high for potential bor-rowers.

Acharya et al. (2011) emphasise the role played by rollover and liq-uidation risk in the Subprime crisis. Similarly to the model developedin the next chapter, they allow banks to borrow liquidity through repoagreements in the money market. In a two-state model, the authorsshow that the pledgeable value of an asset in the bad scenario is lowerthan its fundamental value. The reason is that, when the frequency ofrollover is high, it is unlikely that good news make the value of an assetjump to its good state level by the rollover date. Banks assets have aliquidation cost. Thus, in order to avoid bankruptcy, borrowing banksdo not issue debt with a face value higher than their debt capacity in

the crisis behind the scenes, possibly arranging a takeover by another UK bank.”

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the bad state. Even a small decrease in the fundamental value of theasset at a rollover date may thus cause a large fall in banks debt capac-ity. Such effect is stronger when rollover is frequent and liquidationcosts are high. It can be so important that the market for secured bor-rowing freezes. To the best of my knowledge, the model by Acharyaet al. (2011) is the only one on the Subprime crisis that does not focusneither on early diers nor on changes in lending margins.

Repo margins were undoubtedly an important channel for conta-gion, when lenders updated their estimate of counterparty risk. Brun-nermeier and Pedersen (2009) stress the difference between market liq-uidity and funding liquidity. Whereas the former depends on traders’ability to raise funding liquidity, the latter depends on the terms ofloans such as lending margins. The worsening of lending conditionsmay then interact with market liquidity and start a liquidity spiral.When funding liquidity becomes expensive, solvent institutions maydefault. Such illiquidity risk, addressed by Morris and Shin (2009), is atthe root of the model of contagion in the next chapter.

5 Contagion in the ongoing Eurozone sovereignand banking crisis

At the time of writing, the US banking industry has put the Subprimecrisis behind it. Nevertheless, banks and governments in Europe arestill coping with its consequences. Although European banks are cur-rently liquidity-subsidized through lending facilities by the EuropeanCentral Bank (ECB), they have failed to recover lending to the privatesector. Moreover, creditors have repeatedly penalized governments ofperipheral countries such as Greece, Ireland, Italy, Portugal and Spain(GIIPS).

The US had the largest exposure to subprime mortgages and opaquederivatives. Thus, something specific to European financial marketsshall explain why the crisis had such a long-lasting effect in the Euro-zone. Work by Acharya et al. (2011), Bolton and Jeanne (2011), Brun-nermeier et al. (2011), Gennaioli et al. (2014), Gerlach et al. (2010),Mody and Sandri (2012), Panetta et al. (2011) and Popov and Van Horen(2013) allowed understanding the implications, for a monetary union,

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of a contagion channel that was already recognized in the recent Rus-sian and Argentinian defaults of 1998 and 2001. Such mechanism isunrelated to preference shocks. Contagion is channelled through theinterconnection among sovereigns and the banking industry.

The portfolio of investments held by European banks is heavily bi-ased towards debt issued by European governments. Apart from a“home bias”in the spirit of French and Poterba (1991), regulatory pro-visions are the main driver of such distortion: Popov and Van Horen(2013) point out that, for regulatory purposes connected to the im-plementation of Basel II, the weight associated to government bondsissued in domestic currency is 0%. Such assets are also exempted fromthe limit on large exposures that applies to all other asset holdings.

The European Banking Authority reports that, at the end of 2013,Spanish and Italian banks held 89% of their governments’ debt. Giventhe amount of sovereign bonds held by domestic banks, the cost ofpublic deficit in the Eurozone depends on banks’ ability to refinancesovereign debt. Nonetheless, European banks’ access to financial mar-kets during the crisis hinged on the support provided by the same gov-ernments they finance. The fact that banks enjoy a more or less im-plicit backstop from their home government and are at the same timeproviders of capital through their holding of sovereign bonds is akinto having cross-liabilities in the balance sheets of banks and their gov-ernments. Brunnermeier et al. (2011) defined such linkage betweena country’s public finances and its banking industry the âAIJdiabolicloopâAI.

If a bank faces default its government is likely to bail it out, bothfor the sake of orderly financial markets and to secure its own accessto global financial markets. Reinhart (2011) claims that the bailout ofBear Stearns in March 2008 induced financial markets to believe thatthe US government would use taxpayers’ money to bail out endangeredbanks. Such belief induces moral hazard in the banking industry andis expected to generate excessive risk-taking by financial institutions inthe future. In the aftermath of the Subprime crisis though, the bailoutof Bear Stearns and subsequently that of Anglo Irish in January 2009had also an immediate effect documented by Mody and Sandri (2012).The cost of saving the Irish bank was prohibitive, since financial in-tegration allowed the financial sector of some European countries to

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become huge relatively to the rest of the economy.2 If a governmentbails out banks in such a condition, its ability to (i) repay its debt andto (ii) sustain other financial institutions in trouble is hampered. Inboth cases, the ultimate unintended consequence is that of spreadingthe trouble of one institution to other domestic and possibly foreignbanks.

Reinhart and Rogoff (2009) provide evidence on the relationship be-tween government debt crises and banking crises. Gennaioli et al.(2014) show that sovereign defaults lower financial activity in the de-faulting country. It is not clear whether public defaults are the genuineorigin of a crisis though, as they may actually be the consequence ofweak banking industries. Nevertheless, bad signals on the sustainabil-ity of public debt in the GIIPS countries affected the value of theirbanking sector and that of other European banks that had a big ex-posure to those sovereigns.3 Contagion from the instability of publicfinances to domestic banks was certainly the channel that affected theGreek banking industry.

What happened in the case of Ireland goes a step further and showsthe loop mentioned by Brunnermeier et al. (2011). In the Irish case,public finances were deemed safe as long as domestic banks were sol-vent. However, once the fiscal cost of banks’ bailout appeared unsus-tainable for the Irish economy, the same phenomenon that happened inGreece caused a feedback effect of the deterioration of public financeson Irish banks.

In this section I revise the recent literature that focuses on such case:the difficulty of one or more banks affects sovereign risk and that, giventhe exposure of European banks to their governments via bond hold-ing and implicit/explicit guarantees, affect both the domestic and theforeign banking industry.

2The outstanding debt of the three main Irish banks in 2008 was bigger than thecountry’s GDP.

3Gennaioli et al. (2014) claims that âAIJthese events played a key role in the de-cision to refinance the European Financial Stability Fund (EFSF): averting sovereigndefaults was seen as a key prerequisite to avoid widespread banking crises.âAI

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5.1 The “diabolic loop"

Gennaioli et al. (2014) show that sovereign bonds holding by domesticbanks lowers the cost of public debt. Foreign financers are less con-cerned with a sovereign default since it would dry up domestic liquidityand then investment, output, and tax revenue in the economy. In theirmodel, contagion goes from the government to banks who hold publicbonds. However, the connection between banks and sovereigns is two-way. On the one hand, banks enjoy the explicit and implicit backstopsoffered by their home government. On the other hand, sovereigns havea strong ally in a banking industry that provides funding both to thegovernment and to entrepreneurial projects that result in tax revenues.

Given the size of sovereign bonds holding relatively to banks’ to-tal assets in Europe, and in force of banks’ eligibility to borrow eitherthrough discount window facilities at the ECB or via repurchase agree-ments, the risk of sovereigns’ default lowers banks’ ability to gatherliquidity. As of February 2014, government debt accounted for 5.8%of banks’ assets in the Eurozone.4 At the same time, the lack of fundsprevents governments from putting in place bailout schemes for trou-bled banks, as well as stimulus packages for the rest of the economy.

Acharya et al. (2011) show that bailouts of the financial sector ul-timately caused the rise of sovereign credit risk in Europe, and thatsovereign credit risk increased the credit risk of financial institutions.Abstracting from the possibility of banks’ debt restructuring, the au-thors show that a government may have an incentive to transfer wealthfrom the productive economy to banks. The decrease in banks’ debtcosts a government the issuance of additional sovereign bonds. Thatdilutes the value of outstanding debt, whereas the higher future taxa-tion lowers expectations on economic growth and tax revenue. In suchframework, a bailout initially stabilizes endangered banks. However,if the adverse effect on the value of sovereign bonds is big enough, thevalue of banks’ assets and that of the implicit guarantee from the gov-ernment fall. As this happens, the two risks move together. Such theo-retical result is confirmed by the empirical findings in Mody and Sandri(2012), who find that the cost of financing for European countries ap-

4The same figure to a country-level is 10.2% for Italy, 9.5% in the case of Spain, and7.4% for Portugal, according to data from the ECB.

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peared tied to the outlook of its banking industry since the bailout ofBear Stearns.

Mody and Sandri (2012) look at monthly data to show that since mid-July 2007 the change in spreads of sovereign bonds – which Pagano andVon Thadden (2004) had shown to be white noise – was related to therisk of the financial sector (proxied by CDS spread of US banks). AfterBear Stearns, a linkage emerged between national banking industriesin the Eurozone and the spread of the relative governments over theGerman cost of public debt. The authors show that changes in theprospect of banks’ value began to have an impact on sovereign spreads,after the bailout of the US bank, with a lag of two-three weeks. Thenationalization of Anglo Irish in January 2009 reinforced the marketexpectation that governments would bear high fiscal costs to sustainendangered banks. At the same time, it was clear that such costs werenot affordable. The correlation between banks’ value and sovereignspreads became contemporaneous.

Similarly to the case of domino models, instability of banks andsovereigns reinforce each other in the presence of cross-liabilities. Thus,rather than providing a shelter, the connection between public and pri-vate institutions worsens the crisis. The findings by Mody and Sandri(2012) confirm that the contagion channel works in both directions:sovereign spreads mirror the domestic vulnerabilities of national bank-ing sectors, and this feedback loop has more a severe impact on coun-tries with high debt-to-GDP ratios. Gerlach et al. (2010) find the spec-ular result that sovereign spread increase with the size of the bankingindustry in a crisis, particuarly in the presence of government rescuepackages.

Panetta et al. (2011) measure the impact of public finances on the riskassociated to banks of all troubled Eurozone countries. They find thaton average, in 2010, 30% of the spread was explained by sovereign risk.In the case of the GIIPS countries, such percentage reaches 50%. Theauthors performed the same assessment on pre-crisis data and find thatsovereign risk had a negligible impact on borrowing costs of banks in2006, whereas bank-specific factors explain most of the spread.

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5.2 Cross-border contagion

The fact that banks in the Eurozone hold sovereign bonds issued by dif-ferent European countries is good for diversification purposes ex-ante,but it creates scope for cross-border contagion in the case of default.

Panetta et al. (2011) report that banks from countries with strongpublic finances but with sizeable exposures to sovereigns or banks head-quartered in the PIIGS countries were affected by the instability of thelatter, leading the expected default frequencies of French, German andItalian banks in particular to move together in 2010-2011.

Popov and Van Horen (2013) investigate whether the banking sectormay spread financial distress from defaulting sovereigns to other coun-tries. When banks of European countries in a good financial conditionface the deterioration of their exposure to endangered sovereigns, thataffects negatively the lender country via lower lending to its govern-ment and private sector. The authors provide evidence that lendingby European banks in non-endangered countries recovered slowly af-ter the Subprime crisis when their exposure to endangered countrieswas above the median level. Bolton and Jeanne (2011) show that en-dangered sovereigns in the Eurozone issue too much debt in equilib-rium, whereas countries in good financial conditions do the opposite.In lack of fiscal integration, virtuous governments supply little debt inorder to exploit their monopoly power in case of a flight to quality. Onthe contrary, governments with weaker public finances issue too muchdebt because they do not consider the externality cost faced by othercountries if a crisis materializes. Such inefficient supply of "safety" as apublic good arises regardless of moral hazard created by the possibilityof bailouts.

6 Concluding remarks

Since the first formalization of bank runs was developed in the earlyeighties, the literature on financial crises helped policy makers to un-derstand the sources of instability in the banking industry. The focuswas first on the difficulty. for a single bank, to solve the maturity mis-match between assets and liabilities when depositors faced preferenceshocks. The evidence that runs were related to banks fundamentals

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switched scholars’ attention towards the problem of signalling. At theindustry level, the development of interbank markets allowed banksto cope with idiosyncratic shocks. Nevertheless, it paved the way tocontagion. The latter was first addressed as a domino effect amongbanks balance sheets, and then as the result of sudden sales of marked-to-market collateral. The policy implications of such developmentsallowed western governments and financial institutions to lower thefrequency of crises occurrence.

Yet, the Subprime crisis questioned our understanding of the forcesable to cause distress in the banking industry. There was no run on anybank in the former stages of the turmoil, and the latter is not explainedby the extent of banks interconnectedness. A still unformed strandof the literature has brought its attention away from the issue of earlydiers, and is focusing on funding conditions in the interbank marketwhen liquidity needs stem from the performance of banks’ investmentrather than from depositors’ preferences.

The Subprime crisis began with the discovery that highly structuredfinancial derivatives were overpriced.5 Overly exposed banks lackedthe opportunity to raise from interbank markets the liquidity theyneeded to fulfil their extant commitments. The tightening of repo mar-gin and the hoarding of liquidity by some institutions have been pro-posed as possible explanations. In the next chapter, I develop a modelof contagion that takes no account of early diers and focuses on assetopaqueness, roll-over frequency, and risk constraints to contribute ex-plaining contagion in the crisis of 2007-2009.

5The paternity of this mistake is not addressed in this thesis, although the moralhazard problem with rating agencies and the lack of time series on new custom-madeproducts seem good explanations.

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